abc为非零实数,(a^2+b^2+c^2)(x^2+y^2+z^2)=(ax+by+cz)^2,求证x/a=y/b=z/c

因为：(x^2+y^2+z^2)(a^2+b^2+c^2) =(ax)^2+(bx)^2+(cx)^2+(ay)^2+(by)^2+(cy)^2+(az)^2+(bz)^2+(cz)^2 而：(ax+by+cz)^2=(ax)^2+(by)^2+(cz)^2+2abxy+2acxz+2bcyz 则有：(bx)^2+(cx)^2+(ay)^2+(cy)^2+(az)^2+(bz)^2...